4. The elementary isomerization reaction A C will be carried out in a soft gel...

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4. The elementary isomerization reaction A → C will be carried out in a soft gel that is attached to a flat solid surface. The reactant A is available as part of a gas that also contains oxygen. The reaction only can proceed in the presence of a catalyst that is soluble in the gel but that will oxidize and deactivate if exposed to oxygen. To avoid catalyst oxidation, we propose to impregnate with a catalyst only half of the gel layer (0<x<6, see figure) while maintaining a catalyst-free top layer (8<x<28) that will isolate the catalyst from the gas. In this arrangement, A will diffuse from the gas into the gel and will react to produce C in the reactive layer. The reaction product C will then diffuse toward the gas, since the solid surface (x = 0) is impermeable to both A and C. Both A and C are present at dilute concentrations throughout the gel. The partition of A between the gas and the gel is given by Henry's law: P₁ = HC₁, with H known. The diffusivity of A in the gel is D₁. Diffusion of the catalyst into the nonreactive layer can be neglected. a) Find the steady-state concentration profile of A in the reactive gel layer, in terms of H, D₁, k, 8, and the partial pressure of A in the gas, P.A. b) Find an expression to calculate the molar flux of C that will be transferred to the gas at steady state. 8 Gas containing A Na =? Non-reactive gel layer Reactive gel layer AC, RA=-kCA Solid 4. The elementary isomerization reaction A → C will be carried out in a soft gel that is attached to a flat solid surface. The reactant A is available as part of a gas that also contains oxygen. The reaction only can proceed in the presence of a catalyst that is soluble in the gel but that will oxidize and deactivate if exposed to oxygen. To avoid catalyst oxidation, we propose to impregnate with a catalyst only half of the gel layer (0<x<6, see figure) while maintaining a catalyst-free top layer (8<x<28) that will isolate the catalyst from the gas. In this arrangement, A will diffuse from the gas into the gel and will react to produce C in the reactive layer. The reaction product C will then diffuse toward the gas, since the solid surface (x = 0) is impermeable to both A and C. Both A and C are present at dilute concentrations throughout the gel. The partition of A between the gas and the gel is given by Henry's law: P₁ = HC₁, with H known. The diffusivity of A in the gel is D₁. Diffusion of the catalyst into the nonreactive layer can be neglected. a) Find the steady-state concentration profile of A in the reactive gel layer, in terms of H, D₁, k, 8, and the partial pressure of A in the gas, P.A. b) Find an expression to calculate the molar flux of C that will be transferred to the gas at steady state. 8 Gas containing A Na =? Non-reactive gel layer Reactive gel layer AC, RA=-kCA Solid